Table Of Content1. Introduction
M. H. Brodsky
We live in an electronic era of technological advances based to a large extent on
crystalline semiconductor devices. The marvels of modern semiconductor
technology follow from sound physical knowledge and metallurgical control of
single crystal materials. While semiconductor phenomena are not unique to
crystals, active devices almost always involve single crystals. Amorphous
semiconductors, with the well-established crystalline foundations as a departure
point, offer new frontiers for research and, hopefully, promise for technological
developments.
It is the purpose of this book to provide a cohesive review of the understanding
of electronic phenomena in amorphous semiconductors. For each topic the
authors first present a conceptual framework to place in perspective the trends
and results of current research. A recurrent theme is the distinction between those
phenomena that are amenable to analysis, or at least description, by reference to
already understood crystalline analogies and those effects which are unique, or at
least relatively novel, to the amorphous state.
The most obvious examples of these two distinctive extreme cases are first, the
existence, at least in a gross qualitative sense, of band gaps in amorphous
semiconductors analogous, and close in energy, to the regions forbidden to
electron occupation in crystalline semiconductors ; and second, the lack of long-
range order in the amorphous state which introduces the search to replace the
elegant simplification that periodicity permits in the formal representation of
energy levels in crystals and the allowable transitions between them. Other
phenomena are less clearly distinguishable as being especially analogous or novel.
For example, a conceptually ideal random network of atoms often serves as a
framework for modeling the amorphous state. Then, the question is: Can the
deviations from this ideal be treated as localized defects analogous to point defects
in crystals or are they something new and different?
1.1 Definition of Amorphous Semiconductors
It is easier to define the amorphous state by saying what it is not than by precisely
Specifying what it is. Amorphous semiconductors are noncrystalline. They lack
long-range periodic ordering of their constituent atoms. That is not to say that
2 M.H. Brodsky
amorphous semiconductors are completely disordered on the atomic scale. Local
chemistry provides almost rigorous bond-length, and to a lesser extent, bond-
angle constraints on the nearest-neighbor environment. Unlike amorphous
metals, amorphous semiconductors do not consist of close-packed atoms, but
rather they contain covalently bonded atoms arranged in an open network with
correlations in ordering up to the third or fourth nearest neighbors. The short-
range order is directly responsible for observable semiconductor properties such
as optical absorption edges and activated electrical conductivities.
A distinction should be made between amorphous and polycrystalline
materials. Polycrystalline semiconductors are composed of grains with each grain
containing a periodic array of atoms surrounded by a layer of interconnective or
boundary atoms. For smaller and smaller grains, i.e., microcrystallites, the surface
layer of each grain contains a larger and larger number of atoms relative to the
periodically arrayed interior atoms. Eventually for small enough grains, the
distinction between the interior and surface is lost, and the concept of
microcrystallites with a definable periodic region loses its meaning. While
attempts have been made to model amorphous semiconductors by microcrystal-
lites, it is now generally accepted that network models are more applicable.
However, microclusters of noncrystalline material may exist for some
semiconductors.
The terms "glassy" or "vitreous" are often used synonymously for "amor-
phous" or "noncrystalline." However, in some fields of study, glassy or vitreous
connotes the technical preciseness of a definable thermodynamic phase. The
existence of a glass state, with its glass transition temperature, has been
documented for some chalcogenides but not for the tetrahedrally bonded
amorphous semiconductors. For chalcogenide glasses, this is reflected in the
ability to prepare them from a semiconductor melt by rapid cooling (quenching)
to temperatures below the glass transition temperature. For silicon and the like,
quenching from the melt, which in this case is metallic with a different short-range
order than the desired semiconductor, generally cannot be done rapidly enough
to freeze in an amorphous atomic arrangement. Polycrystallinity is the more
common result.
Amorphous semiconductors that cannot be prepared directly from the melt
are usually fabricated in the form of thin films by an atomic deposition procedure
such as evaporation, sputtering, chemical vapor deposition, plasma decom-
position of gases, or electroplating. Sometimes ion bombardment of crystals is
used to leave an amorphous layer in the collision trail of.the ions.
Once prepared, a material is empirically defined to be amorphous if its
diffraction pattern consists of diffuse rings (halos) rather than sharply defined
Bragg rings or spots characteristic ofpolycrystalline or single crystal solids. While
mixtures of amorphous and crystalline materials can exist, there does not seem to
be a continuous transition from one to the other. Where measured, conversion
from amorphous to crystalline takes place by nucleation and growth rather than
by homogeneous atomic rearrangement.
noitcudortnI 3
1.2 Current and Future Trends
Amorphous semiconductors, while forming a single area of study with some
unifying ideas, often is divided into two subfields, the tetrahedrally coordinated
siliconlike materials and the chalcogenide glasses. Arsenic, from column V of the
periodic table, forms a bridge between the two classes of materials. This book
deals with the common methods and theories that today place particular
emphasis on defects in materials from either class. In this section, a perspective si
given on how the present situation has developed.
1.2.1 Amorphous Silicon Defects and Passivation
Amorphous silicon when nominally pure is permeated with dangling bonds as
evidenced by a detectable electron spin resonance (ESR) signal from about
5 X 1019 spins cm- .3 While the origin and properties of the dangling bond spins
are interesting in themselves, they generally obscure many phenomena of interest
to semiconductor physicists. For example, the electron energy levels of the
dangling bonds lie in between the valence (bonding) states and conduction
(antibonding) states of the fully paired, bonded electrons. These states in the gap
contribute to optical absorption and electrical conduction processes, masking the
measurement of an energy gap by either process. Further, there is a large density of
gap states which act as fast nonradiative recombination centers, with the result
that photoconductivity or photoluminescence is uninterestingly small in pure
amorphous silicon. Finally, the Fermi level, which is essentially pinned by the gap
states, does not move significantly when trace impurities of the conventional
shallow donor or acceptor types (e.g., phosphorus or boron, respectively) are
incorporated. Since normal annealing procedures reduce the ESR signal, the
electrical conductivity and the tailing of the optical absorption edge, it was
originally, and optimistically, assumed that "ideal" amorphous silicon might be
approached either by annealing or by slowly depositing onto substrates at
elevated temperatures. The assumption here was that the annealing effects were
due to the healing of dangling bonds by reconstruction and rearrangement of the
amorphous network and not merely due to contamination. More recently it was
established that under clean conditions the annealing effects are minimal and that
amorphous silicon will crystallize before all the dangling bonds are removed.
Thus, ideal, pure amorphous silicon seems to exist in concept only.
If dangling silicon bonds cannot be paired to each other, the opportunity still
exists to pair them with other atomic orbitals. Hydrogen appears to be suitable for
this purpose. Other atoms, e.g., oxygen, nitrogen, fluorine, etc., may also aid the
passivation process. Following the success of the glow discharge plasma
decomposition ofsilane, several other procedures have evolved for incorporating
hydrogen into amorphous silicon. These include reactive sputtering with a
hydrogen-containing gas, proton implantation, and postdeposition treatment in
a hydrogen plasma. In all cases it si presumed that hydrogen passivates the
4 M.H. yksdorB
dangling bonds thereby revealing the interesting properties of intrinsic amor-
phous silicon, somewhat mediated by alloying effects.
Many intrinsic properties of hydrogenated amorphous silicon have been
studied to date. These include the thermally activated conductivity, the optical
absorption edge, photoluminescence, electroluminescence, and photoconduc-
tivity. In addition, the standard shallow donors and acceptors have been shown to
dope hydrogenated amorphous silicon to be n type or p type, respectively. The
phenomena and configurations of interest and import to single crystal silicon,
now become amenable to study with amorphous silicon. Extrinsic conductivity,
thermopower, Hall effect, and photoconductivity, amongst others, are all dopant-
dependent phenomena with crystalline analogs that have been measured for
amorphous silicon. Often the results are interpretable in terms of processes
previously described for crystals. Sometimes - the sign of the Hall effect has been
the most notable example - the crystalline analogy does not work.
Schottky barrier and pnjunction diodes are two devicelike configurations that
have been constructed with amorphous silicon. When operated as solar cells these
diodes behave to some extent like the corresponding crystal devices. Even
complicated transistorlike structures have been proposed, though practical
realizations are not yet here.
The simple thesis of passivated dangling bonds si appealing, but it si not the
whole story. Hydrogen or other additives might, besides passivating gap states,
play active roles by, for example, enlarging the band gap (alloying with Si),
sensitizing photoexcited processes, changing the lattice electron coupling, etc.
How much hydrogenation si needed to reveal the most interesting phenomena si
still an open question. It appears that more than just the paramagnetic centers,
.e ,.g weak or otherwise reconstructed bonds, pick up hydrogen. Efforts continue
to quantify the process.
In summary, amorphous silicon as a semiconductor with interesting
semiconductor properties has been revealed by the hydrogenation of dangling
and weak bonds. What the future holds si the study of the revealed host, the
revelation process, doping and associated effects, devicelike configurations, and,
eventually, useful devices.
1.2.2 Chaicogenide Glasses dna Proper Valence
In contrast to amorphous silicon and the other group IV tetrahedrally bonded
semiconductors, the amorphous chalcogens and chalcogenides do not exhibit a
dangling bond spin resonance signal in their clean, as-prepared state. Pervasive
diamagnetism rather than paramagnetism si the general rule. Chalcogens with
their twofold coordination and lone-pair orbitals offer the network the dual
channels of structural and electronic flexibility for removal of dangling bonds. As
a consequence, a typical chalcogenide has a relatively sharp optical absorption
edge, a single electrical activation energy, and efficient photoexcited conductivity
and luminescence. llA these properties are characteristic of a well-defined and
noitcudortnI 5
clean forbidden gap. Nevertheless, field-effect and doping experiments indicate
that the Fermi level of a chalcogenide glass si nearly pinned. Luminescent
emission occurs at subband gap energies. Paramagnetism can be photoexcited at
low temperatures. llA of these latter effects are normally characteristic of states in
the gap, and until recently posed an unsolved paradox. The resolution of the
paradox was found in the concept of negative correlation energies of gap states,
thereby leading to pairing of electrons with opposite spins. In essence, distortions
of the host network are possible so that bonded, paired electrons are favored over
uncorrelated, gap-filling, single electron states. Competitive models exist for the
microscopics of paired states. Theoretical and experimental activity now focuses
on how to identify the microscopic pairings, be they charged dangling bonds,
valence alternation pairs, or other arrangements yet to be proposed. The path for
understanding of intrinsic semiconductor phenomena in chalcogenides now
appears here within the framework of flexible structural coordination and
available lone pair electrons.
1.2.3 etaidemretnI sesaC
Between the extremes of the column IV tetrahedrally coordinated amorphous ,iS
Ge, and SiC and the twofold coordinated column 1V chalcogens in elemental and
COmpound or alloy glasses lie two other classes of amorphous semiconductors
with some properties characteristic each of the two extremes. These are the
amorphous group V semiconductors, e.g., arsenic, and III V semiconductors,
e.g., GaAs. These pnictide-containing amorphous semiconductors do not have
dense concentrations of paramagnetic dangling bonds, but often do have a small
residual dark ESR signal (< 6101 spins cm-3), particularly when prepared by
quanching to cryogenic temperatures. Network rigidity si higher than for
ehalcogenides because of higher nearest-neighbor coordinations, but less than for
group VI semiconductors because of possible lower coordination and lone pair
orbitals. At present, investigations of semiconductors of the l lI-V and V type have
not progressed as far as for the prototypical siliconlike or chalcogenide
amorphous semiconductors. Undoubtedly there si room here for future study and
testing of the hypotheses put forth for the conceptually simpler extreme cases.
1.3 Organization of the Book
In this chapter, we have given an introduction to previous developments on the
topics of most recent interest, tracing them to emphasize the reasons for the
current activity on defect states and passivation techniques, doping, and solar
cells. Analogies to crystalline phenomena were drawn and those effects that are
almost unique to amorphous semiconductors were pointed out. The next two
chapters continue to provide an introductory framework to the book.
6 M.H. Brodsky
Chapter 2 places in perspective the various theoretical approaches relating
energy eigenstates to the spatial structure of amorphous systems. All types of
approaches, from brute force numerical methods to sophisticated formalisms are
reviewed with respect to how well the different methods can hope to answer the
most relevant questions about states near the gap, namely, localization and
transitions to extended states.
Chapter 3 focuses on states in the gap and what are called "defects" in fully
coordinated network models for amorphous semiconductors. Of principal
concern are the consequences of electron pairing which gives diamagnetic rather
than paramagnetic gap states in chalcogenide glasses.
Next follows a series of chapters, each dealing with a particular class of
phenomena. In Chap. 4, a framework is put forth for understanding the optical
absorption from defects in the gap, band tails, and interband transitions.
Examples of all three types of observations are given.
Chapter 5 uses band models to sort electrical conduction in amorphous
semiconductors into three competitive channels analogous to the three regimes of
optical absorption in the previous chapter : localized states at the Fermi energy,
localized states in band tails near the mobility edge, and extended state
conduction. In addition to the temperature-dependent conductivity, experimen-
tal results for thermoelectric power, ac conductivity, transient conductivity, and
photoconductivity are reviewed for chalcogenides and interpreted in terms of
band models or the alternative small-polaron picture.
Chapter 6 reviews photoluminescent phenomena in both siliconlike and
chalcogenide amorphous semiconductors. After sifting through the influence of
preparation conditions, the author puts forth models for the underlying physical
mechanisms.
Chapter 7 introduces the concept of hard and soft centers as the origin of the
electron spin resonance signals in pure and hydrogenated amorphous silicon,
respectively. Then experimentally observed spin-dependent recombination
effects are described and interpreted.
Chapter 8 identifies those elements of the short-range order that are best
studied by X-ray absorption fine structure (EXAFS) or infrared and Raman
vibrational spectroscopy, two techniques of current interest. A survey of the
vibrational spectra in various classes of elemental and compound amorphous
semiconductors is given. This is followed by recent EXAFS and vibration results
on local environments, bonding defects, and wrong bonds.
Chapter 9 covers the preparation and properties of doped amorphous silicon.
The emphasis is on a self-consistent picture in terms of the density-of-states
distribution deduced from field-effect measurements. The special aspects of the
potential barrier in amorphous semiconductor junctions are presented.
Finally Chap. 01 deals with those properties of doped and undoped
amorphous silicon that are relevant to photovoltaic solar cells. State-of-the-art
photovoltaic characteristics are discussed within the context of preparation
parameters, and a model analysis of cell operation is given.
Introduction 7
Although a multi-author volume such as this will naturally have a variety of
styles and individual approaches, all of the authors have tried to incorporate some
common structure to their expositions. First the conceptual framework is set, then
the calculations or experimental results are examined within this conceptual
context. Further, recurring reference is made to crystalline analogies or novel
aspects of the amorphous state, as is appropriate.
2. Theory of Electronic States
in Amorphous Semiconductors ~
B. Kramer and D. Weaire
With 21 serugiF
Our subject is, as the clich6 goes, still in its infancy. Nevertheless it has matured
considerably over the last ten years. Most theorists now realize that structure
necessarily lies at the heart of the problem of the theory of electronic properties
of amorphous semiconductors. As a corollary of this, we must recognize that
the questions which it poses are ill defined, for our knowledge of the structure of
these materials is rather limited. They are also intrinsically difficult. There is no
longer such a tendency to conceal this by such formal devices as the Gubanov
Transformation (which transforms the theory of crystals into the theory of
amorphous solids, and, presumably, pumpkins into stagecoaches).
While the best work in the area of band structure of crystals emphasizes
quantitative results, one can hardly hope to emulate this for amorphous solids.
Qualitative understanding is still to be achieved in this area.
Many authors have tried to classify and to idealize the varieties of disorder
in sotids, and particularly amorphous solids. Typical categories are structural,
compositional, cellular, quantitative, topological ..... Such schemes are usually
tied to a particular theoretical framework, such as the tight-binding method.
The complexity of the problem is such that the study of idealized model
systems, in which disorder is more easily identified, quantified, and controlled,
provides a very useful first step in the understanding of the properties of a real
amorphous semiconductor. Thus, for instance, the "many-impurity system"
2.1 provides insight into the behavior of heavily doped semiconductors 2.2
and the dependence of band-tailing upon disorder. The model of "purely
topological disorder", as represented by the Hamiltonian used by Thorpe and
Weaire (Sect. 2.2.1) allows a discussion of the behavior of bands and band gaps
in tetrahedrally bonded amorphous semiconductors. The Anderson
Hamiltonian (Sect. 2.3.1) represents "pure compositional disorder" and is the
key model for the understanding of electron localization in disordered systems.
Such idealizations are useful as the skeletal basis of an understanding of
electronic properties. Sooner or later, less idealized models must be analyzed,
but without such a basis they can hardly be intelligently treated.
The primary quantity of interest is the density of electronic energy levels.
What si the connection between the distribution of energy eigenvalues and the
spatial structure of a disordered system ? In particular, how do band gaps survive
ni the absence of long-range order? What is the shape of the density of states
1 Work supported yb eht ecneicS hcraeseR .licnuoC
01 .B remarK dna .D eriaeW
near the band edges? What is the role of the short-range order in determining the
shape of the bands? Are there any significant features related to defects and
dangling bonds ?
Of equal importance is the nature of the electronic wave functions. They
may be localized or extended, depending on the system parameters and on the
corresponding energy. Localization usually appears in the band tails and
strongly affects the transport properties of a material. Although the concept of
localization is now quite a familiar one, many questions, particularly dealing
with quantitative aspects of the problem, are still open. What are the conditions
for electron localization? What are the positions of the "mobility edges" for a
given system? What is the nature of the transition from localized to extended
states ? How does the electrical conductivity behave at this "'Anderson transition"?
The variety of responses to these questions provides a study in contrasting
styles, ranging from crude number crunching to elegant formalism. Our
intention in this chapter is to gather together rather more of these separate
threads than has been done in the past, although whether we succeed in
weaving them into a pattern is another matter ! Our initial emphasis will be on
the techniques themselves (Sect. 2.1) and the reader who is uninterested in their
finer points may find it more profitable to proceed to their applications and
results (Sects. 2.2, .)3
Correlation effects 2.3 may in some cases be crucial in the interpretation
of experimental data 2.4. The theory of these is still in a very qualitative stage
2.5-15 and goes beyond the scope of this article.
2.1 Theoretical Methods
The most systematic and elegant work on disordered systems has been devoted
to the alloy problem. Although the relevance of this to amorphous solids is
indirect and there are excellent reviews 2.16, 17, we shall include it within the
scope of this section, since it is the source of many key ideas.
In the case of Anderson localization there is little choice - almost all work
to date has been on "alloy" Hamiltonians.
2.1.1 General Theorems
We begin with some examples of general theorems which can be invoked in this
area.
Starting from the Schr/3dinger equation of the tight-binding type,
~F H,icj = ~vc;, (2.1)
J
the methods and theorems of matrix analysis can be applied. In (2.1), H 0 are the
matrix elements of the Hamiltonian in an orthonormal set of basis functions i),
Theory of cinortcelE States ni Amorphous srotcudnocimeS 11
each attached to an atom site i, '}C are the coefficients of the vth eigenstates, and
,,E is the corresponding eigenenergy. Following the theorems of Peron,
Frobenius, and Gerschgorin (see, e.g., 2.18-20), the eigenvalue spectrum of
~;H is bounded above and below:
-Em.x<E,,~Em,,x . (2.2)
The maximum eigenvalue Ema x is bounded by the condition
min VH <E <max ~Hij. (2.3)
i} ~. ij : max : {i}
3 J
As an example, we consider a simple, topologically disordered system as
described by the Hamiltonian
H=V li)(jl (V>O). (2.4)
i,j
nearest
neighbor~
Let Z be the number of nearest neighbors connected to a given atom by the
transfer matrix element .V According to the relations (2.2) and (2.3), the
spectrum of eigenvalues is bounded above and below by _+ZK respectively,
since each row and column of H u contains exactly Z nonzero matrix elements
.V The bandwidth is finite and cannot be greater than 2ZV. There are many
such general results for the spectra of topologically and quantitatively disor-
dered systems using more realistic forms of the tight-binding Hamiltonian (2.1),
including intra- and interatomic interactions. These include the Lifshitz bounds
for a binary alloy 2.1 as sketched in Fig. 1.2 and the bounds established for
the sp 3 Hamiltonian by Weaire and Thorpe 2.21 which we shall discuss in
more detail in Sect. 2.2.1.
2.1.2 Approximation Techniques
In the theory of periodic systems the use of Green's functions often seems to
obscure what would otherwise be obvious. However, many of the most
significant developments in the theory of disordered systems have been framed
in terms of Green's functions and some facility in dealing with them is
indispensable to a proper understanding of the subject.
a) Green's Functions and the Density of States
Using the energy-dependent one-electron Green's function defined by
G(z)=(z- H)-1, the density of states may be written as
n(E) = - 1 lim Tr {Im {G(E + it/)}}. (2.5)
1~ q~O
